A weighted mean (or weighted average) is like an ordinary mean, but the observations don't contribute equally - more emphasis is placed on some data values than others; they are weighted by a bigger or smaller amount than 1/n.

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Compare Log-Normal Distributions

I am looking at distributions for the fuel consumption of vehicles in the US and I have two sets of data: Data Set 1 - This is a dataset for the fuel consumption of all vehicles made available for ...
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89 views

Weighted average of measurements with unequal errors

Suppose I have the numbers below. Consider them as results of some measurement. ...
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7 views

Appropriate weighting for averages

What is the appropriate (or the advantages of disadvantages for each) measure for weighting mortality rates across countries: total population or total number of deaths? For example, if you have ...
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32 views

Weighting on tables

I have a question about terminology. Suppose I have data categorized by three factors A, B, and C, with cell means $\bar{y}_{ijk}$ and cell frequencies $n_{ijk}$, where $i$, $j$, and $k$ index A, B, ...
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Weighted Standard Deviation vs. Weighted Regression Standard Error

This is an R question. I have $n$ observations of the variable $y$, with each observation, $i$, weighted by $w(i)$. Each $w(i)$ weight falls between zero and 1, with the sum of the weights, ...
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How to bootstrap confidence of a weighted measure?

I have a large data set of 20M observations with 20+ measures for each observation (people). Additionally I have a set of weights that reflect the racial population where each person lives. For ...
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Estimated Treatment Effect in the full sample is not between the estimates of the stratified samples?

I am estimating the relationship between students' math scores and using a supplemental math software. I've adjusted for some demographic variables in the model. In my first model, I use the full ...
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How to symmetrically adjust data by removing certain value

Say I have a data set in the following format: {a:200, b: 100; c:400} The sum of a, b and c equals 700. Now, I have another value which is supposed to be the actual total say 500. How do I adjust ...
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Computationally cheap estimation of the mode from 2D samples

I say 'mode' in the title – perhaps there's something more appropriate I can find. Here's my problem: A person is in a $100\mathrm m$ by $500\mathrm m$ space. I have about 100 samples randomly ...
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Aggregating based on inverse probability weight

I have a data set that includes life quality indices for many cities. I want to aggregate the indices to the metropolitan level. Since some cities in each metro area are missing, the data set provides ...
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How do I determine the appropriate “weight” of a point in fantasy basketball?

For fantasy basketball, I want to quantify a player's output based on his Points, Rebounds, Assists, Steals, 3s, and Blocks production. Let's pretend that over the course of an imaginary basketball ...
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Hypothesis test for difference between domain means with weighted data

I have a large dataset that is weighted due to: probability proportional to size sampling, & disproportionate stratification. I would like to compare the means for two different domains ...
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How do I determine the significance of a difference in weighted averages from a Likert-type survey question?

I have multiple survey questions that give respondents 4 Likert-type options for a response to qualify their knowledge/skill in a particular area. I have calculated a weighted average (and divided by ...
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Number of occurrences gives higher weights

I have this algorithm that I'm implementing that I need to change to give it a better accuracy. To give you an idea of the problem, I have a a bunch of lists that contain items and all items in these ...
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Paired test: many repetitions, few subjects

I have a situation similar to this: 9 normal-sighted subjects are each tested under two conditions: say, with and without spectacles (of a fixed power) and asked to reach towards an object many times ...
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how to use global weights to update local ones

I have a population of data points. Each data point expresses a different name. Each such name belongs to a different ethnicity, say {A, B, C, D, E}, with a probability. The sum of probabilities for a ...
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Average difference in averages and t-test

I'm currently working with some individual level data and have run up against a wall in figuring out the best way to analyse it. Let me describe: We have a sample of N=9000 Physicians. For each ...
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Calculate scores for users with varying activity

I have a web application which allows users to take questions. Ultimately I store the following data: 1) Questions attempted by each user 2) Questions correct by each user 3) Avg. Time per user for ...
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How to use global weights when normalizing a mean value?

This is a very silly question, however, it confuses me a lot! Let's suppose that each observation consists of the prob of $A$ and the prob of $B$, with values $1/2$ and $1/2$ respectively. Also, ...
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League table with weighted result

I have a simple set of data indicating completion rates that I want to present as a ranked/league table. The data available is that for every visit of a person, a plan document should be completed by ...
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81 views

Averaging across independent strata: confidence interval

I've $k$ independent strata, with populations $n_1,\dots,n_k$, and have estimated the mean in each stratum $\bar{x_1}, \dots \bar{x_k}$ and obtained the standard errors $se_1,\dots,se_k$ (using STATA ...
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122 views

Best fit of weighted mean?

The title might be somewhat misleading. I am trying to solve the following optimization problem and do not find any clues. Can any one help? I have a sequence of $n$ observation $s_i$. Each ...
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Weighting datapoints by uncertainty - asymmetric CIs

I have several estimates obtained using different softwares, these programs give me an estimate as well as a 95% confidence interval. However, these CIs are not symmetric around my point estimates, ...